Sharp Morawetz estimates

We prove sharp Morawetz estimates — global in time with a singular weight in the spatial variables — for the linear wave, Klein-Gordon, and Schrödinger equations, for which we can characterise the maximisers. We also prove refined inequalities with respect to the angular integrability.     

Formal (4+1) Cycloaddition and Enantioselective Michael–Henry Cascade Reactions To Synthesize Spiro[4,5]decanes and Spirooxindole Polycycles

Spiro[4,5]decanes and polycyclic compounds bearing spiro[4,5]decane systems are important biofunctional molecules. Described are diastereoselective formal (4+1) cycloaddition reactions to afford oxindole-functionalized spiro[4,5]decanes and organocatalytic enantioselective Michael–Henry cascade reactions of the (4+1) cycloaddition products to generate spirooxindole polycyclic derivatives bearing the spiro[4,5]decane system. Spiro[4,5]decanes bearing oxindoles containing three stereogenic centers and spirooxindole polycycles having seven stereogenic centers, including two all-carbon chiral quaternary centers and one tetrasubstituted chiral carbon center, were obtained with high diastereo- and enantioselectivities.     

Applications of Clifford’s Geometric Algebra

We survey the development of Clifford’s geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly demonstrate the benefit of developing problem solutions in a unified framework for algebra and geometry with the widest possible scope: from quantum computing and electromagnetism to satellite navigation, from neural computing to camera geometry, image processing, robotics and beyond.     

Preparation of dibromopyridines having -(CH2)m-SO3Na groups as monomers for new polypyridines

Dibromopyridines or dibromopyridone with -(CH₂)_m-SO₃Na group(s) has been prepared via the reactions of the corresponding dibromopyridines with -OH and -NH₂ groups with sultone. These compounds were converted into polymers with the -(CH₂)_m-SO₃H groups via organometallic polycondensation. The polymer showed proton conducting properties and high stability toward oxidation.     

Finite Time Extinction for Nonlinear Schrödinger Equation in 1D and 2D

We consider a nonlinear Schrödinger equation with power nonlinearity, either on a compact manifold without boundary, or on the whole space in the presence of harmonic confinement, in space dimension one and two. Up to introducing an extra superlinear damping to prevent finite time blow up, we show that the presence of a sublinear damping always leads to finite time extinction of the solution in 1D, and that the same phenomenon is present in the case of small mass initial data in 2D.     

Effects of Bis(aromatic) Pendants on Recognition of Nucleobase Thymine by Zn2+ -1,4,7,10-tetraazacyclododecane (Zn2+ -cyclen)

We have previously shown that the nucleobase thymine binding to Zn²⁺ -cyclen (cyclen=1,4,7,10-tetraazacyclododecane) complex became stronger by appending acridine, naphthalene, or quinoline rings to the cyclen. Amongst these, the pendant bis((1-naphthyl)methyl) or bis((4-quinolyl)methyl) groups yielded the most effective thymine-recognizing Zn²⁺ -cyclen complexes [J. Am. Chem. Soc., 121 (1999) 5426]. The present study was undertaken to find causes of the bis(aromatic) ring effect by X-ray crystal structure analysis and NMR studies. The crystal structure of the Zn²⁺ -bis((1-naphthyl)methyl)-cyclen complex with a deprotonated 1-methylthymine (1-MeT) failed to show the anticipated evidence for the double ~ - ~ stacking interactions between the two naphthalenes and the Zn 2+ -bound 1-MeT m (1-MeT m =N(3')-deprotonated 1-MeT). Crystal data: formula C₃₆ H₄₇ N₇ O₇ Zn, M r =755.19, monoclinic, space group P2₁/ c (No. 14), a =15.438(2) Å, b =14.093(3) Å, c =16.726(2) Å, g =90.53(1) V =3638.7(8) Å 3 Z =4, R =0.035, R _w =0.049. However, the ¹H NMR studies of Zn²⁼ -bis((4-quinolyl)methyl)-cyclen with 1-MeT in varying H₂O/CH₃ CN solution showed increasing upfield shifts of Me(5') and H(6') of the Zn²⁺ -bound 1-MeT in more aqueous media, indicating that the double intercalation with the two quinolines became more significant in more protic environments. We conclude that the double ~ - ~ stacking effect accounts for the enhanced recognition of thymine base by the appended bis((1-naphthyl)methyl) or bis((4-quinolinyl)methyl) groups.     

Electrothermal atomic absorption spectrometric determination of cadmium in environmental samples with niobium wire preconcentration method

A preconcentration method by adsorption of cadmium on a niobium wire was developed for the environmental waters, followed by electrothermal atomic absorption spectrometry with a tungsten tube atomizer. After the preconcentration, the niobium wire was directly inserted into the tungsten tube atomizer. In the preconcentration (adsorption) process of cadmium, the optimal immersing time was 60?s. The effects of large amounts of concomitants on the preconcentration of cadmium were evaluated. When 10³–10⁴ fold excess of matrix elements existed in aqueous solution at pH 4 and 9, the cadmium response was profoundly affected by the matrix elements. However, the cadmium absorption signal was not significantly influenced at pH 7. Therefore, pH 7 was selected for the application into the real environmental samples. Under the optimal conditions, the detection limit (3S/N) for cadmium by the niobium wire preconcentration method was 7.0?pg?mL^?1 and the relative standard deviation was 6.8%. The method with preconcentration on a niobium wire was applied to the determination of cadmium in water and proved to be sensitive, simple and convenient. Because this preconcentration method can be utilized in the in situ treatment of trace cadmium in environmental water samples, it was unnecessary to carry the water samples to the analytical work place. The technique was shown to be useful for the determination of cadmium in environmental water samples at 0.1–1?µg?L^?1 levels.     

Hyrtimomines,indole alkaloids from Okinawan marine sponges Hyrtios spp.

Six new indole alkaloids, hyrtimomines F–K (1–6), were isolated from Okinawan marine sponges Hyrtios spp. The structures of 1–6 were elucidated on the basis of spectroscopic analysis. Hyrtimomine F (1) is a structurally unique bisindole alkaloid possessing an α-keto-?-caprolactam ring, while hyrtimomine G (2) is a symmetrical bisindole alkaloid. Hyrtimomines H–K (3–6) are indole alkaloids possessing β-carboline skeleton with an imidazolium unit. Antimicrobial activities of hyrtimomines F–K (1–6) were evaluated.